Joan is $62$ years of age and has lived in her home for $22$ years. She paid $$150,000$ for the home, and she recently sold it for $$450,000.$ She added a room to the house by converting a garage to a den, at a cost of $$20,000.$ The real estate broker charged a $6\%$ commission for the sale. What is Joan's taxable gain from the transaction $($ignore any Section $121$ exclusion$)?$